You are allowed to have up to 12 outlets(receptacles and lights) on a circuit. If you can maintain less than 12 by tapping off and existing receptacle then that is fine.
Another consideration is what is going to be used on this circuit. If you might be using heaters or and AC then a new circuit might be a good idea.

You are allowed to have up to 12 outlets(receptacles and lights) on a circuit. If you can maintain less than 12 by tapping off and existing receptacle then that is fine.
Another consideration is what is going to be used on this circuit. If you might be using heaters or and AC then a new circuit might be a good idea.

IIRC, Ray C. Mullin's interpretation of the '99 NEC said 10 to 20 on a circuit was practical and that the NEC doesn't spec this number.

I would run a new circuit for sure. Laundry area, which would be the washing machine zone, is supposed be on its own circuit. It could be fine if it was done like before that code came into effect, but I would not add anything new to this circuit.